modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...

, a regular modal logic is a modal logic containing (as axiom or theorem) the duality of the modal operators:

\Diamond A \leftrightarrow \lnot\Box\lnot A

and closed under the rule

\frac.

Every

normal modal logic In logic, a normal modal logic is a set ''L'' of modal formulas such that ''L'' contains: * All propositional tautologies; * All instances of the Kripke schema: \Box(A\to B)\to(\Box A\to\Box B) and it is closed under: * Detachment rule (''modus po ...

is regular, and every regular modal logic is classical.

References

*Chellas, Brian. ''Modal Logic: An Introduction''. Cambridge University Press, 1980. Logic Modal logic {{logic-stub